The CF is automatically defaulting back to the root index.cfm file instead of the home/authenticate.cfm without ever processing the home/authenticate.cfm file. No errors are generated or displayed. The code in the home/authenticate.cfm file is:

<cfoutput>hi</cfoutput>

The desired output is to have “Hi” written in the div with the ID of “results”.
I have run the same post method using “home/response.asp” as the url which returns simple html. It works perfectly. The issue seems to be narrowed down to ColdFusion or Fusebox. We are using ColdFusion Version: 7,0,0,91690 and Fusebox V.4. 1 on IIS 7 web server.
Do you have any suggestions on how I can make the .cfm file work?

Questions like this are tough to troubleshoot because there's no telling the application configuration you're working with. That said, there is one early easy test you can do.

I see in your jQuery call that you're calling "home/authenticate.cfm" and you mentioned that you have two separate sites. Presumably the jQuery is on one of the sites and, if so, the call is to the other site, right? One site calling another site likely needs more than "home/authenticate.cfm" to successfully get there. What you have is a partial path that will have the calling app trying to access "home/authenticate.cfm" within itself.

Consider putting the full URL to the site that contains "home/authenticate.cfm" into your jQuery call and see what you get.